New York Journal of Mathematics
Volume 15 (2009) 301-318


C. Robinson Edward Raja

Distal actions and ergodic actions on compact groups

Published: July 30, 2009
Keywords: Compact groups, nilpotent groups, automorphisms, distal, ergodic
Subject: 22B05, 22C05, 37A15, 37B05

Let K be a compact metrizable group and Γ be a group of automorphisms of K. We first show that each α ∈ Γ is distal on K implies Γ itself is distal on K, a local to global correspondence provided Γ is a generalized \bar{FC}-group or K is a connected finite-dimensional group. We also prove a connection between distality and ergodicity which is used to show that ergodic actions of nilpotent groups on compact connected finite-dimensional abelian groups contains ergodic automorphisms.


Partially supported by NSERC postdoctoral fellowship

Author information

Stat-Math Unit, Indian Statistical Institute, 8th Mile Mysore Road, Bangalore 560 059. India